Define "sniper"
If by sniper you mean you want to cover four holes with a silver dollar at 500 yards you might be up the chreek wihtout a paddle and a hole in the boat for your price.
If however you want to hit a melon at 500 yards most good hunting rifle will do just fine. Thats all a sniper rifle really is, a hunting rifle that is spiffed up, accurized a bit, and has a really good scope.
Get a 500 dollar hunting rifle, tweak it (bed it, float it, adjust trigger, etc.), and a really good scope and wham, there's your spiper rifle for under a thousand bucks.
That all changes if by sniper you mean competition and want 1moa at many hundreds of yards.